Theorem oteq1d 3753

Description: Equality deduction for ordered triples. (Contributed by Mario Carneiro, 11-Jan-2017.)

Hypothesis

Ref	Expression
oteq1d.1	|- ( ph -> A = B )

Assertion

Ref	Expression
oteq1d	|- ( ph -> <. A , C , D >. = <. B , C , D >. )

Proof of Theorem oteq1d

Step	Hyp	Ref	Expression
1		oteq1d.1	. 2 |- ( ph -> A = B )
2		oteq1 3750	. 2 |- ( A = B -> <. A , C , D >. = <. B , C , D >. )
3	1, 2	syl 14	1 |- ( ph -> <. A , C , D >. = <. B , C , D >. )

Syntax hints:   -> wi 4   = wceq 1335   <.cotp 3564

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139

This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-v 2714  df-un 3106  df-sn 3566  df-pr 3567  df-op 3569  df-ot 3570

This theorem is referenced by:  oteq123d  3756